[EM] PAR is awesome part 1/2: FBC?

[C.Benham]

On 11/13/2016 3:35 AM, Jameson Quinn wrote:

> What I mean is that if you take a non-election-theorist, present an 
> election scenario to them, explain who won and why, and ask how they 
> would strategize in the place of voter X, they are more likely to 
> suggest counterproductive strategies, and less likely to see any 
> strategies that actually might work, in Condorcet than in Bucklin-like 
> systems.
>

The strategy incentives for Condorcet voting methods vary widely. Some 
have a random-fill incentive while others have a truncation incentive. 
Some have
a stronger or weaker incentive to equal-top rank than others, and some 
are more vulnerable to Burial than others.

Smith//Approval has a truncation incentive like Bucklin's, only less 
strong. In addition Bucklin has an equal-top rank/rate incentive.  I 
don't see the problem.

BTW, why does it matter if "non-election-theorists" when asked suggest 
"counter-productive strategies"?  Shouldn't we be encouraging sincere 
voting?
If they don't want to do that, why can't they just take the strategy 
advice of their favourites?

35: C >> A=B
33: A>B >> C
32: B>A >> C

> In Smith//approval, one vote alone would shift the above honest 
> election; so the fact that it does not in PAR is indeed notable.

I don't see why.  The example I gave just happened to have a close CW.  
PAR seems to give an A=B tie unless (as I assume) it breaks tied final
scores in favour of the "leader" (A).

> In particular: in PAR, there is no way for the B voters to strategize 
> such that they win the above election, while still ensuring that C 
> does not win no matter what the A voters do.

Of course, that is why it's called a "chicken dilemma".  In what method 
/can/ "the B voters to strategize such that they win the above election, 
while still ensuring that C does not win no matter what the A voters do" ??

> MJ passes IIA. PAR fails it, as you say, but passes LIIA.

As do some Condorcet methods. It isn't one of the criteria I care much 
about.

As I understand it, IIA can only be met by methods that fail Majority 
(like positional methods that pretend that the voters' ratings are on 
some scale independent of the
candidates).   MJ  is a variety of Median Ratings which is normally 
claimed to meet Majority.

I would be a bit surprised if IIA can be met by a method (such as MJ and 
Bucklin) by a method that fails Irrelevant Ballots Independence.

There is some rubbish about Independence of Irrelevant Alternatives 
(IIA) on Electowiki.  I'll address that in a later post.

Chris Benham


On 11/13/2016 3:35 AM, Jameson Quinn wrote:
>
>
> 2016-11-12 10:45 GMT-05:00 C.Benham <cbenham at adam.com.au 
> <mailto:cbenham at adam.com.au>>:
>
>     On 11/12/2016 7:53 AM, Jameson Quinn wrote:
>>
>>
>>     2016-11-11 12:50 GMT-05:00 C.Benham <cbenham at adam.com.au
>>     <mailto:cbenham at adam.com.au>>:
>>
>>         On 11/11/2016 10:14 PM, Jameson Quinn wrote:
>>
>>>         I think that simple PAR is close enough to FBC compliance to
>>>         be an acceptable proposal.
>>
>>         I'm afraid I can't see any value in "close enough" to FBC
>>         compliance. The point of FBC is to give an absolute guarantee
>>         to (possibly uninformed
>>         and not strategically savvy) greater-evil fearing voters.
>>
>>
>>     Yes. The guarantee you can give is "as long as the world is
>>     somewhere in this restricted domain — that is, essentially, as
>>     long as there are no Condorcet cycles and each voter naturally
>>     rejects at least one of the 3 frontrunners — this method meets
>>     FBC". This is much broader than any guarantee you could give for
>>     a typical non-FBC method. For instance, with IRV, the best you
>>     could say would be "as long as your favorite is eliminated early
>>     or wins overall, you don't have to betray them", which unlike
>>     PAR's guarantee is not something which could ever be generally
>>     true about all real elections for all factions.
>>
>     C: I have in mind voters who are inclined to Compromise, and so
>     it's /absolute guarantee/ or it's nothing.   Smith//Approval also
>     has a much lower Compromise incentive
>     than does IRV  (which in turn has a much much lower Compromise
>     incentive then FPP).
>
>
>>
>>
>>
>>>         It elects the "correct" winner in a chicken dilemma
>>>         scenario, naive/honest/strategyless ballots, without a
>>>         "slippery slope" (though of course, this is no longer a
>>>         strong Nash equilibrium). 
>>
>>         How do you have a "chicken dilemma scenario" with
>>         "naive/honest/strategyless ballots" ?
>>
>>         35: C >> A=B
>>         33: A>B >> C
>>         32: B >> A=C  (sincere is B>A >> C)
>>
>>         In this CD scenario your method elects B  in violation of the
>>         CD criterion.
>>
>>
>>     You're suggesting that the sincere preferences are
>>
>>     35: C >> A=B
>>     33: A>B >> C
>>     32: B>A >> C
>>
>>
>     C:  I'm not "suggesting". I'm stating.
>>
>>     If you are 1 of the B>A>>C voters considering whether to
>>     strategically vote B>>A=C, you have no strong motivation to do
>>     so, because your vote alone is not enough to shift the winner to
>>     B. This is what I mean by "no slippery slope".
>>
>>
>     C: One "vote alone" is very rarely enough to do anything, so I
>     suppose no-one has a "strong motivation" to vote.
>
>
> In Smith//approval, one vote alone would shift the above honest 
> election; so the fact that it does not in PAR is indeed notable.
>
> In particular: in PAR, there is no way for the B voters to strategize 
> such that they win the above election, while still ensuring that C 
> does not win no matter what the A voters do. This "safe" strategizing 
> is grease on the slippery slope.
>
>
>>
>>
>>     I believe that in the election you gave, there is no way to tell
>>     what the sincere preferences are.
>>
>>
>
>     C: From just the information on the ballots, of course not (like
>     any election).
>>
>>     Perhaps the B voters are strategically truncating A; perhaps the
>>     C voters are strategically truncating B. So the "correct winner"
>>     could be either A or B, but is almost certainly not C.
>
>     C: By "correct winner" I assume you mean the sincere CW. But there
>     is reason to assume there is one. And if the B voters are actively
>     Burying C, it could be C.
>
>>     The "CD criterion" requires the system to elect C, merely to
>>     punish the B voters; I think that's perverse, because, among
>>     other things, it means that a system does badly with center
>>     squeeze, allowing the C faction to strategize and win.
>>
>     C: No, it merely says "not B".  But CD + Plurality say that it
>     must be C.
>>
>>
>>         Since you are apparently now content to do without FBC 
>>         compliance  and you imply that electing the CW is a good thing,
>>         why don't you advocate a method that meets the Condorcet
>>         criterion?
>>
>>         What is wrong with Smith//Approval?  Or Forest's nearly
>>         equivalent Max Covered Approval?
>>
>>
>>     Largely, it's because I think that Condorcet systems are
>>     strategically counterintuitive, and hard to present results in. I
>>     think that will lead to more strategy than a system like PAR.
>>     That's because PAR can make guarantees that Condorcet systems can't.
>>
>     C: Such as?  What exactly does "strategically counter-intuitive"
>     mean?  An example?
>
>
> What I mean is that if you take a non-election-theorist, present an 
> election scenario to them, explain who won and why, and ask how they 
> would strategize in the place of voter X, they are more likely to 
> suggest counterproductive strategies, and less likely to see any 
> strategies that actually might work, in Condorcet than in Bucklin-like 
> systems.
>
>
>>
>>     In a system like MJ or Score, you can give a number to each
>>     candidate, based on their own ratings alone, and the higher
>>     number wins. That is an easy way to get monotonicity, FBC, and IIA.
>>
>>     In Condorcet, no candidate has any number except in relation to
>>     all other candidates. That's good for passing the Condorcet
>>     criterion (obviously) but it breaks FBC and IIA.
>>
>     C:  Your method and MJ fail IIA.
>
>
> MJ passes IIA. PAR fails it, as you say, but passes LIIA.
>
>
> Prefer Accept Reject (PAR) voting works as follows:
>
>  1. *Voters can Prefer, Accept, or Reject each candidate.* Blanks
>     count as "Reject" if no rival is explicitly rejected; otherwise,
>     blank is "Accept".
>  2. *Candidates with at least 25% Prefer, and no more than 50% reject,
>     are "viable"*. The most-preferred viable candidate (if any) is the
>     leader.
>  3. Each "prefer" is worth 1 point. For viable candidates, each
>     "accept" on a ballot which doesn't prefer the leader is also worth
>     1 point. *Most points wins.*
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20161113/5c3713b6/attachment-0001.htm>